A Direct Discontinuous Galerkin Finite Element Method And Superconvergence Analysis For A Singularly Perturbed Probelm

In this paper,the finite elment method is used to deal with one-dimensional singular perturbation problem.Applying the direct discontinuous finite element method to the model problem,a numerical scheme for the two-point boundary value problem is constructed.After rigorous numerical analysis,the stability,orthogonality and boundedness of the scheme are obtained.The optimal error estimates including logarithmic factors are obtained on Shishkin meshes.At the same time,the superconvergence properties of other adaptive grids are explored.Under the discrete energy norm,the optimal error estimates of higher order are obtained.The numerical examples are consistent with the theoretical analysis.